Identifying Nodes and Anti-Nodes of an Axially Vibrating Bar with Lumped Mass

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Engineering (HMC)

Publication Date



In a recent letter to the editor, Batan and Gurgoze [1] noted mistakes that were contained in the paper by Cutchins [2]. Specifically, they observed errors that are caused by numerical evaluations of the frequency equation of a fixed-free axially vibrating bar with a lumped mass attached at a point along the span of the bar (see Figure 1). The frequency equation and the corresponding mode shapes of teh system of Figure 1 are given in reference [2]. Using another solver, Batan and Gurgoze recalculated the first three eigenfrequencies of the system of Figure 1 as a function of the location of the lumped mass. They noted that their frequency curves are similar in shape to those obtained in reference [2]. However, unlike the results given in reference [2], the minima of their frequency curves shift with varying values of the lumped mass. Comparing the two curves in Figure 2 of reference [1], it is also noted that the maxima of the two curves occur at the same lumped mass location. While Batan and Gurgoze used the minima of the frequency curves to highlight the difference between the two set of results, it is interesting to note that the location of these maxima and local minimum of the frequency curves also reveal certain physical characteristics of the system.

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© 1997 Academic Press. All rights reserved.